One-Dimensional Numerical Investigation of a Cylindrical Micro-Combustor Applying Electrohydrodynamics Effect

Transcription

1 One-Dmensonal Numercal Investgaton of a Cylndrcal Mcro-Combustor Applyng Electrohydrodynamcs Effect Abstract In ths paper, a one-dmensonal numercal approach s used to study the effect of applyng electrohydrodynamcs on the temperature and speces mass fracton profles along the mcrocombustor. Premxed mxture s H -Ar wth a mult-step chemstry (9 speces and 9 reactons). In the mcro-scale combuston because of the ncreasng rato of area-to-volume, thermal and radcal quenchng mechansms are mportant. Also, there s a sgnfcant heat loss from the combustor walls. By nsertng a number of electrodes nto mcro-combustor and applyng hgh voltage to them corona dscharge occurs. hs leads n movng of nduced ons toward natural molecules and colldng wth them. So ths phenomenon causes the movement of the molecules and reattaches the flow to the walls. It ncreases the velocty near the walls that reduces the wall boundary layer. Consequently, applyng electrohydrodynamcs mechansm can enhance the temperature profle n the mcrocombustor. Ultmately, t prevents the flame quenchng n mcrocombustor. eywords mcro-combustor,electrohydrodynamcs, temperature profle, wall quenchng I. INRODUCION N the recent researches, many MEMS-based (Mcro IElectromechancal Systems) devces such as mcro gas turbnes [], mcro recprocatng engnes [], mcro thermophotovoltac systems [3, 4], mcro fuel cells [5] etc. need a hgh-densty mcro-power supply to operate. Mcro combuston s one of the best ways to provde ths power. he superorty of ths mcro-power source to conventonal batteres s ts hgher energy densty n comparson wth batteres. One of the basc components of a mcro-power system s the mcro combustor that uses the oxdant-fuel mxture to release desred energy. In the present wor, because of hgh area-to-volume rato, both thermal and radcal quenchng mechansms are mportant. Fernandez-Pello [6] revewed some of the technologcal detals related to mcro combuston and mcro power generaton devces. Modelng and smulaton of the mcro-scale combuston systems has been dscussed by many researches recently. Although L et al [7] concluded that the reactng flow n the mcro scale combuston s D n nature, but D smulaton s used n many researches to evaluate the effect of dfferent parameters on mcro scale combuston. P. Behrouzna s the M.Sc. student wth the Mechancal Engneerng Department, Sharf Unversty of echnology, ehran, Iran (e-mal: pooya_behroozna@mech.sharf.edu). A. Iran R. s the Ph.D. student wth the Mechancal Engneerng Department, Sharf Unversty of echnology, ehran, Iran (e-mal: abran@mech.sharf.edu). M.H. Sad s the Professor of the Mechancal Engneerng Department, Sharf Unversty of echnology, ehran, Iran (P.O. Box , e-mal: saman@ sharf.edu). World Academy of Scence, Engneerng and echnology 67 0 Behrouzna P., Iran R. A., Sad M.H. Also, asare and Vlachos [8] showed that the results of both the D and D numercal smulaton are n good agreements. L et al [9] developed a D model to demonstrate the effect of combustor sze, fuel property, fuel-ar equvalence rato and unburned mxture temperature on the heat loss rato and heat recrculaton rato. hey concluded that the hydrogen s more sutable n comparson wth the methane and propane due to ts hgher flame temperature and thnner flame thcness. Another ey ssue of ths wor s electrohydrodynamcs (EHD). Bushnel [0] and Mal et al. [] reported several onc wnd veloctes affected drag reducton. Soetomo [] demonstrated expermentally that nduced AC and DC corona dscharge along a flat plate, n the case of flow veloctes up to m/s, results n the drag reducton. Soldat [3] observed numercally that ncreasng EHD flow ntensty reduces the drag. Also, the heat transfer enhancement n natural convecton by usng EHD ntated n 96 by Lyouds and Yu [4]. hey studed natural convecton between a cold cylnder and a hot wre at center of cylnder. Also, they appled a non-unform electrc feld. hey concluded that heat transfer enhances wth secondary flow produced by electrc force. Yabe et al. [5] developed a model for nvestgaton of the dssoluton and the expermental corona wnd effect. In ther research, they used an slender wre for anode and a plate for cathode. hey observed that there are postve ons n the whole of the regon except near hot wre. hey estmated electrc potental by numercal methods. Consequently, they showed that the corona wnd produced by Coulomb force nduced to ons and natural gas molecules. In the present wor, a D numercal method s used to nvestgate EHD applcaton affectng combuston n mcro scales. A home-made D transent code s developed to do smulatons. he burnng mxture s H ar wth a detaled reacton mechansm of 9 speces and 9 reactons. Furthermore, heat transfer wth the surroundng along the combustor walls s consdered. emperature and speces mass fracton profles are plotted for dfferent heat transfer coeffcents and dfferent number of electrodes at steady state condton. As can be seen from the results of the present wor, they used to locate the flame zone n mcro-scales. Also, effect of varous parameters on thermal behavor of a mcro combustor can be compared and only hghly effectve of them choose to desgn. For example n many applcatons, generatng heat near the regon of nterest s mportant n devces. Consequently, locatng the pont wth the hghest temperature s desred []. hs phenomenon s smlar to a jet wth low velocty flows to earth electrode and applcable to complex geometres for enhancng heat transfer. 05

2 World Academy of Scence, Engneerng and echnology 67 0 In ths method, there are no excess sound, vbraton and spar. Corona can be n the form of radaton or flowng wth the effect of exertng postve voltage. Flowng form almost occurs when hgh or low voltage exerts that there s onzaton state but radaton form occurs when medum voltage exerts and t observes n the steady state flows. Negatve voltage results are dfferent wth these results completely, however, snce postve voltage lead to phenomenonn becomes stable and also has many applcaton, almost t used n research. In hgh powers, joule heatng that converts electrc energy to heat energy leads to reducton the effcency. Fg. shows the physcs of the corona mechansm. (b) Fg. (a) Electrcal breadown; (b) recombnaton and upeep of the dscharge [9] Fg. Corona dscharge ntaton [9] Corona wnd leads to rot the boundary layer and consequently mproves the heat transfer n the mcro- hs phenomenon combustor whch prevents wall quenchng. called EHD-enhanced heat and mass transfer. EHD Advantages are as follow:. Implementaton of ths method s smple and only needs one electrc converter and electrodes.. Heat and mass transfer coeffcents can regulate smply by electrc feld ntensty.. In many applcatons consumpton of electrc energy s low. Postve and negatve corona mechansms seem le together. A natural atom or molecule n the regon wth hgh electrc feld (for example a regon wth hgh electrc potental near the sharp electrode) onzed by an external motve (for example photon nteractons). Fg. showss corona mechansm. (a) So electrc feld affects these onzed partcles and prevents the adheson of partcles together. Moreover, t can accelerate the partcles whch enhance the netcs energy. Wth effect of energzed electrons wth hgh charge to mass rato and hgh acceleraton, a number of produced ons mpact to natural atoms. hs chan contnues when an electron avalanche produces. he postve and the negatve corona are based on ths electron avalanche. Postve corona ntates from the regon wth hgh electrc potental. In ths type, the sharp electrode has postve voltage and the electrode wth lower curvature has ground voltage. he onzed Electrons move to the electrode wth hgh curvature. In the postve corona, the producton of the secondary electrons for avalanche s contnung n the flud and n the regon out of the plasma. he electrons whch are produce by the onzaton of natural gas molecules attract to sharp electrode and plasma. herefore, many avalanches produce. Postve corona regon has two sectons. One of these sectons s the Inner regon. hs regon nvolves postve ons, electron, electron avalanche and plasma. he outer regon s the other secton of postve corona that nvolves a number of postve ons wth low velocty movng to postve electrode. he two regons have a common zone. In ths zone secondary electrons that produced by photons exted by plasma move to plasma regon. Inner regon called plasma regon and outer regon called one-pole. Establshment of negatvee corona s more complex than postve corona. hs type of corona also ntates by producton of external onzaton. Ionzed Electrons wth natural gas, are unsutable for producton of secondary electrons that produce electron avalanche; because these electrons move to postve electrode. However, for negatve corona the way of producton of the secondary electrons s photoelectrc phenomenon from electrode surface. Energy source for released electrons s photon wth hgh energy. Prncple dfference between postve and negatve corona s the method of producng secondary electrons. In the postve corona, secondary electrons produce by gases around the 06

3 World Academy of Scence, Engneerng and echnology 67 0 plasma regon and released electrons move to plasma, but n the negatve corona, they are produced by electrode and move out. Negatve corona can dvde by three regons. In the nner regon hgh energzed electrons mpact wth natural atoms and cause producton of the electron avalanche. In the outer regon the negatve ons produced. In the mddle regon, there s no suffcent energy to produce the electron avalanche, but t s a partton of plasma and has plasma propertes. Inner regon s the onzed plasma and the mddle regon s non-onzed plasma. Also, outer regon s one-charge regon. II. COMPUAIONAL DOMAIN, FORMULAION AND SOLUION MEHOD A. Computatonal Doman In ths study, a cylndrcal reactor s used as shown schematcally n Fg. 3. As can be seen from the Fg. 3, the combustor dameter s very small n comparson wth the reactor length, therefore the temperature n radal drecton s assumed to be constant. herefore, t s n good agreement wth the D assumpton. he heat transfer to the upstream by the sold wall conducton s neglected n the present wor. In ths wor, one and two electrodes have been used n combustor transversely that electrode postons are from outward of plane toward n the plane. Electrodes are shown n the Fg.3 wth bold ponts at center of combustor. Fg. 3 Schematc of cylndrcal reactor and electrodes used n ths wor B. Ehd Equatons From electrc feld and charge densty relatons due to corona effect, ths equaton produced:.( ε E) = q () 0 he relaton between electrc feld densty and voltage s: E = V () And the charge contnuty equaton s:. J = 0 (3) Where J s charge densty has been obtaned from ohm formula: J = qbe + qu (4) wo rght hand sde terms of (4) are on movablty and charge dsplacement respectvely. From order of magntude, Ion veloctes, be, are hgher order of magntude compare to the flud velocty, u. thus, we can relnqush the second rght term of (4). Also, () combned wth () and therefore ths equaton obtaned: V = (5) ε In addton, f all of these equatons combne together, an mportant equaton obtaned: q = ε ( V. q) (6) Boundary condtons on wre electrodes are: q = q 0 and V = V0 (7) Where V 0 s the appled voltage to wre electrodes and q 0 s charge densty on surface of wre electrode that obtaned from pee formula [0]: lwj p 5 q0 = 0 (8) δ πbrf [30δ + 9( ) ] r Where δ s 0P, 0 =93, P 0 =. [0] 5, combustor P0 temperature, P combustor pressure, J p average electrc current densty on plates, l w wre to wre dstance, b moblty, r corona wre radus and f s roughness. Roughness for clean wres s. Usng corona dscharge n ths wor adds a term nto the energy equaton generally: ( u ) qbe + = α + (9) t x x ρc q However, ths term adds to specal forward energy equatons that dscuss n next sectons. C. D Model Equatons and Soluton Method Contnuty, energy transport and speces mass transport equatons n the transent D model form an Advecton- Dffuson-Reacton (ADR) system of equatons. Because we assumed that wall of combustor s nert, the gas radaton and the wor of vscous and pressure forces can be neglected. hus, energy and mass balance equatons are as follows: d ρc p + C pu C p, D Y ρ ρ = = (0). ( λ ) h w & = dy ρ + ( ρuy ) = ( ρd Y ) + w& W () In the present wor, the flow s lamnar and the pressure loss along the combustor s neglected. Also, another assumpton of ths wor s that the reactants and products speces are deal gases. herefore, densty and velocty are obtaned from the followng equatons: = Y R W () u ρ P = p 07

4 World Academy of Scence, Engneerng and echnology 67 0 u u ( Area) ( Area) ρ n n n j = (3) ρ j j In the above equatons, energy equaton, speces mass transport equatons and reacton rates are coupled to each other. Soluton of above system of equatons wth conventonal CFD methods causes some dffculty. In addton, a mult-step chemstry mechansm s used. hus, the reacton rate calculaton results n a stff system of ODEs. In the present wor, to solve these equatons smultaneously, the Operator Splttng (OS) method s used. he method of ths soluton s dvdng a system nto subsystems that can be ntegrated n tme [6]. Splttng technque has two man schemes: frst order scheme (lnear), and second or hgher order scheme (non-lnear). he above equatons are nonlnear. herefore, the Strang Splttng method whch s preferable for nonlnear stff system of PDEs, s used. hs method dvdes the nonlnear stff systems of PDEs nto two non-stff systems of PDEs and two stff systems of ODEs. Stff systems of ODEs are solved by VODE method (Varablecoeffcent Ordnary Dfferental Equaton) [7]. he soluton procedure s as follows:. Advecton-Dffuson (A-D): In ths step, the solutons are energy and mass balance equatons wthout the reacton terms for the frst half of tme-step: * d ρcp + ρcpu ρcp, D Y.( λ ) qbe = + = * * (4) * dy * * ρ + ( ρuy ) = ( ρd Y ) (5) Where tn < t < t and ntal condtons are as below: n+ n ( ), ( ) t = Y t = Y (6) * * n n n. Reacton (R): In ths step, wth consderaton of only the reacton term n the whole tme-step, the equatons reduce to: ** d ρc p = h w & (7) = ** dy ρ = w& W (8) where tn < t < t n + and ntal condtons are as below: ** ( t ) * ** ( ) * n = t, Y tn = Y t n+ n+ (9). Advecton-Dffuson (A-D): hs step s smlar to step, but the flow feld s solved for the nd half of tme-step: *** d *** *** ρcp + ρcpu ρcp, D Y =. ( λ ) + qbe (0) = *** dy *** *** ρ + ( ρuy ) = ( ρd Y ) () where t < t < t n + and ntal condtons are as follows: n+ *** t ** ( ) *** ** = tn, Y t = Y ( tn ) () n+ n+ After all these three steps are solved for one tme step, the new solutons are set as the ntal condtons of next tmestep: n+ *** n+ = t, Y = Y *** t (3) ( ) ( ) n+ n+ he above procedure s repeated teratvely untl reachng steady state. o solve the A-D equatons, the power-law scheme wth an LU decomposton solver s used. D. Combuston Modelng A mult-step and general reacton mechansm s consdered: ' " ν χ ν χ = =, ( =,,... I) (4) he rate of producton of each speces s: I & (5) ω = ν q, ( =,..., ) = where the rght hand sde terms are: ' " = (6) ν ν ν ' " ν ν q = a [ X ] f [ X ] r [ X ] (7) = = = where the forward reacton rate constants calculate from the Arrhenus equaton: β E f = A exp( ) (8) R c he reverse reacton rate constants are: f r = (9) S C P ν atm = C = P ( ) R (30) o o S H P = exp[ ] R R (3) o o S S = ν R R (3) H R o = H o = ν (33) = R a o a ln a a7 R = (34) o H a a3 a4 3 a5 4 a6 = a (35) R a a 08

5 World Academy of Scence, Engneerng and echnology 67 0 he above equatons form a stff system that solved by usng VODE method. E. hermophyscal Propertes In ths wor, as used by asare and Vlachos research [8], the thermal dffusvty of the gas mxture s assumed to be constant. hs value s consdered to be. Gas phase thermal conductvty s calculated from the mxture average formula [8]: λ = λ x + = X = λ (36) hermal conductvty of H, O, HO and N speces s assumed to be a polynomal functon of temperature. he polynomal coeffcents are curve fttng at the temperature range ( ). hermal conductvtes of the above speces are calculated from below relatons: 3 8 λh = (37) = λo λh O = = λn (38) (39) (40) A computatonal grd ndependency test s performed. he temperature profle for 7, 4 and nodes are shown n Fg. 4. As can be seen from ths result, 4 nodes are preferable number of grds []. emperature [] Nodes 4 Nodes Nodes x [m] Fg. 4 emperature profles for dfferent number of grds [] emperature profles wth dfferent convectve heat transfer coeffcents ( h=5,0,0 W/(m.) ) are exhbted n Fg hese fgures show that applyng electrodes can enhance temperature profle and also usng two electrodes s better than usng one electrode to enhance t. In spte of enhancng heat transfer wth EHD method, energy added n mcro-combustor by electrodes s hgh enough that ts temperature rses to desrable value. Also, t can be seen that maxmum and average temperature along the mcro-combustor enhanced usng EHD method. Also molar heat capacty s obtaned from the followng equaton: o C p 3 4 a a a3 a4 a5 R = (4) he above coeffcents are smlar to the coeffcents used n (34) and (35). III. RESULS AND DISCUSSION he effect of convectve heat transfer coeffcent on temperature and mole fractons profles are nvestgated n the followng three cases. One of these cases s checng the mcro-combustor wthout applyng EHD method. Another case s applyng EHD method usng one electrode n mcrocombustor that s located at the center of t and the latter case s applyng EHD wth two electrodes that are located at one quarter and three quarter of mcro-combustor length respectvely. Because of mcro-scales doman and to prevent meltng of mcro-electrodes, appled voltage must not be much hgh. For ths reason, n ths study, appled voltage s 000 volt. Fg. 5 emperature profle at h=5 ( 09

6 World Academy of Scence, Engneerng and echnology 67 0 Fg. 6 emperature profle at h=0 ( Fg. 8 [OH] mole fracton profle at h=5 ( Alternatvely, [OH] mole fracton n dfferent convectve heat transfer coeffcents usng three cases are shown n Fg It can be seen that ths mole fracton profle s hgher n the case of applyng EHD than usng wthout EHD method. Also, usng two electrodes can ncrease ths profle more than usng one electrode. he average temperatures n the case of h=5 are 70, 430 and 570 for the case of no EHD, one electrode and two electrodes, respectvely. hese values n the case of h=0 are 00, 30, 60 and n the case of h=0 are 75, 94, 0. Fg. 9 [OH] mole fracton profle at h=0 ( Fg. 7 emperature profle at h=0 ( Fg. 0 [OH] mole fracton profle at h=0 ( Furthermore, [ ] and [ ] mole fractons n dfferent convectve heat transfer coeffcents n aforementoned three cases are shown n Fg

7 World Academy of Scence, Engneerng and echnology 67 0 Fg. [ ] mole fracton profle at h=5 ( Fg. 4 [ ] mole fracton profle at h=5 ( Fg. [ ] mole fracton profle at h=0 ( Fg. 5 [ ] mole fracton profle at h=0 ( Fg. 3 [ ] mole fracton profle at h=0 ( Fg. 6 [ ] mole fracton profle at h=0 ( IV. CONCLUSION In the present wor, one dmensonal numercal approach has been studed to nvestgate the effect of applyng EHD method on the mcro-combustor temperature profle and flame

8 World Academy of Scence, Engneerng and echnology 67 0 quenchng. hree cases performed n ths wor namely usng one electrode, two electrodes and the case of no EHD. hese cases appled to dfference convectve heat transfer coeffcents. A mult-step chemstry mechansm for H -ar mxture s consdered. Also, the lateral convecton heat transfer wth the surroundng s consdered. he numercal results show that usng EHD method can enhance the maxmum and average temperature n the mcrocombustor and consequently, prevent flame quenchng by ths temperature rse along mcro-combustor. Also n order to ncrease temperature profle, applyng two electrodes s more effectve than one electrode. In addton, [OH] mole fracton profle rses wth applyng electrodes along mcro-combustor. By applyng ths method, there s no need for usng catalyst to prevent flame quenchng. Moreover, results llustrate that flame zone s a thn regon that located near the mcro-combustor nlet and ncreasng the convecton heat transfer coeffcent reduces the temperature and radcal speces concentratons profles n the flame zone. [7] Brown P.N., Byrne G.D. and Hndmarsh A. C., 988, VODE, a varable-coeffcent ODE solver, SIAM Journal of Scentfc and Statstcal Computng. [8] Marthur S., ondon P.. and Saxena S.C., Molecular physcs, :569 (967). [9] Junhong Chen, "Drect-Current Corona Enhanced Chemcal Reactons", Ph.D. hess, Unversty of Mnnesota, USA. August 00. [0] Pee, F.W., Delectrc Phenomena n hgh-voltage engneerng, McGraw-Hll, New Yor, (99). [] Iran R. A., Saedamr M., Sad M.S., Sad M.H. and Shaf M.B., one dmensonal numercal nvestgaton of a cylndrcal mcro-combustor, ASME Summer Heat ransfer Conference July 9-3, 009, San Francsco, Calforna USA. REFERENCES [] Watz I.A., Gauba G. and Yang S.., 998, Combustors for mcro-gas turbne engnes, Journal of Fluds Engneerng, 0 (998) [] Jn P., Gao Y.L., Lu N., an J.B. and Jang., 006, Desgn and fabrcaton of alumna mcro recprocatng engne, Journal of Physcs: conference seres, 48 (006) [3] Lee.H. and won O.C., 008, Studes on a heat-recrculatng mcroemtter for a mcro thermophotovoltac system, Combuston and Flame, 53 (008) 6-7. [4] Yang W.M., Chou S.., Shu C., Xue H., L Z.W., L D.. and Pan J.F., 003, Mcroscale combuston research for applcaton to mcro thermophotovoltac systems, Energy Converson and Management, 44 (003) [5] Vahab M. and Ahbar M.H., 009, hree-dmensonal smulaton and optmzaton of an sothermal PROX mcroreactor for fuel cell applcatons, Internatonal Journal of Hydrogen Energy, 34 (009) [6] Fernandez-Pello A.C., 00, Mcro-power generaton usng combuston: Issues and approaches, wenty-nnth Internatonal Symposum on Combuston, July -6, 00, Sapporo, Japan. [7] L Z.W., Chou S.., Shu C., Xue H. and Yang W.M., 005, Characterstcs of premxed flame n mcrocombustors wth dfferent dameters, Appled hermal Engneerng, 5 (005) 7-8. [8] asare N.S. and Vlachos D.G., 007, Optmal reactor dmensons for homogenous combuston n small channels, Catalyss oday, 0 (007) [9] L J., Chou S.., L Z. and Yang W., 008, Development of D model for the analyss of heat transport n cylndrcal mcro-combustors, Appled hermal Engneerng. [0] D. Bushnell, urbulent drag reducton for external flows, AIAA Paper , Reno, USA, January 983. [] M.R. Mal, L. Wensten, M. Hussan, Ion wnd drag reducton, AIAA Paper , Reno, USA, January 983. [] F. Soetomo, he nfluence of hgh-voltage dscharge on flat plate drag at low Reynolds number ar flow, M. S. hess, Iowa State Unversty, Ames, Iowa, 99. [3] A. Soldat, S. Banerjee, urbulence modfcaton by large scale organzed electrohydrodynamc flows, Phys. Fluds 0 (7) (998) [4] Lyouds, P.S., Yu, C.P., 96, he nfluence of electrostrctve forces n natural thermal convecton, nternatonal journal of heat and mass transfer, 6, [5] Yabe, A., Mor, Y., Hjtata,., EHD study of corona wnd between wre and plate electrodes, AIAA J., 6 (978) [6] Sportsse B., 000, An analyss of operatng splttng technques n the stff case, Journal of Computatonal Physcs, 6,